FINITE SPEED OF PROPAGATION OF SOLUTIONS FOR SOME QUASILINEAR HIGHER ORDER PARABOLIC EQUATIONS WITH DOUBLY STRONG DEGENERATION

1991 ◽  
Vol 11 (2) ◽  
pp. 164-174 ◽  
Author(s):  
Jingxue Yin
Keyword(s):  
Parabolic Equations ◽  
Higher Order ◽  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Speed Of Propagation ◽  
Higher Order Parabolic Equations ◽  
Strong Degeneration

scholarly journals Finite speed of propagation and asymptotic rates for some nonlinear higher order parabolic equations with absorption

1986 ◽  
Vol 104 (1-2) ◽  
pp. 1-19 ◽  
Author(s):  
F. Bernis
Keyword(s):  
Decay Rates ◽  
Dirichlet Boundary Conditions ◽  
Weighted Energy Method ◽  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Speed Of Propagation ◽  
Image Position ◽  
Higher Order Parabolic Equations ◽  
Quasilinear Elliptic ◽  
Uniformly Bounded

SynopsisThe “energy solutions” to the equationhave finite speed of propagation if l < q < 2 or l < r < 2. If 1 <r <2 (Vq <1) support u(· t) is uniformly bounded for t >0 (localisation property) and if q<2 ≦ r, sharp upper bounds of the interface (or free boundary) are obtained. We use a weighted energy method, the weights being powers of the distance to a variable half-space. We also study decay rates as t→∞ and extinction in finite time for bounded and unbounded domains (with null Dirichlet boundary conditions). Our equation includes the porous media equation with absorption. Analogous results hold if (−Δ)m is replaced by an appropriate quasilinear elliptic operator.

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